Year 12 Function Notation, Composites and Inverses Worksheet — Level 2 — Answers
Answer sheet with worked solutions for the Year 12 functions worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · FunctionsYear 12 Function Notation, Composites and Inverses Worksheet — Level 2 — Answers
f(x) notation means "the value of the function at x". For a composite, substitute the inner function into the outer one. For an inverse, swap x and y and solve for y.
1.If f(x) = −3x2 + 6x + 6, find f(3).
Answer: −3
- Replace x with 3: −3(3)2 + 6(3) + 6
- = −3
2.f(x) = −4x + 4 and g(x) = 5x − 3. Find f(g(x)) in simplest form.
Answer: −20x + 16
- f(g(x)) = −4(5x − 3) + 4
- = −20x + 16
3.f(x) = 2x − 5 and g(x) = x − 3. Find g(f(x)) in simplest form.
Answer: 2x − 8
- g(f(x)) = 1(2x − 5) − 3
- = 2x − 8
4.f(x) = 2x − 1 and g(x) = 2x + 5. Find g(f(x)) in simplest form.
Answer: 4x + 3
- g(f(x)) = 2(2x − 1) + 5
- = 4x + 3
5.f(x) = 2x + 3 and g(x) = x − 2. Find f(g(x)) in simplest form.
Answer: 2x − 1
- f(g(x)) = 2(x − 2) + 3
- = 2x − 1
6.f(x) = −x − 2 and g(x) = 5x + 1. Find g(f(x)) in simplest form.
Answer: −5x − 9
- g(f(x)) = 5(−x − 2) + 1
- = −5x − 9
7.f(x) = x + 1 and g(x) = 3x + 4. Find f(g(x)) in simplest form.
Answer: 3x + 5
- f(g(x)) = 1(3x + 4) + 1
- = 3x + 5
8.If f(x) = 3x2 − x − 8, find f(5).
Answer: 62
- Replace x with 5: 3(5)2 − (5) − 8
- = 62
9.If f(x) = 3x2 − x + 6, find f(−3).
Answer: 36
- Replace x with −3: 3(−3)2 − (−3) + 6
- = 36
10.f(x) = 3x and g(x) = 4x + 1. Find g(f(x)) in simplest form.
Answer: 12x + 1
- g(f(x)) = 4(3x) + 1
- = 12x + 1
11.If f(x) = 4x2 + 2x − 5, find f(−2).
Answer: 7
- Replace x with −2: 4(−2)2 + 2(−2) − 5
- = 7
12.f(x) = −4x − 1 and g(x) = 4x − 6. Find g(f(x)) in simplest form.
Answer: −16x − 10
- g(f(x)) = 4(−4x − 1) − 6
- = −16x − 10
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